On an additive decomposition of the BLUE in a multiple-partitioned linear model

Necessary and sufficient conditions are derived for the BLUE in a general multiple-partitioned linear model {y,X1β1+⋯+Xkβk,σ2Σ} to be the sum of the BLUEs under the kk small models {y,X1β1,σ2Σ}, ……, {y,Xkβk,σ2Σ}. Some consequences and further research topics are also given.